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Ecological Modelling 221 (2010) 2491–2500

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

n agent-based model of red colobus resources and disease dynamics implicatesey resource sites as hot spots of disease transmission

yler R. Bonnell a,∗, Raja R. Senguptaa, Colin A. Chapmanb,c, Tony L. Goldbergd

Dept. of Geography, McGill University, 805 Sherbrooke St. W., Montreal, QC, Canada H3A 2K6Dept. of Anthropology & McGill School of Environment, McGill University, Montreal, QC, CanadaWildlife Conservation Society, Bronx, NY, USADept. of Pathobiological Sciences, School of Veterinary Medicine, University of Wisconsin-Madison, Madison, WI, USA

r t i c l e i n f o

rticle history:eceived 13 April 2010eceived in revised form 12 July 2010ccepted 21 July 2010vailable online 17 August 2010

eywords:

a b s t r a c t

The effect of anthropogenic landscape change on disease in wildlife populations represents a growingconservation and public health concern. Red colobus monkeys (Procolobus rufomitratus), an endangeredprimate species, are particularly susceptible to habitat alteration and have been the focus of a greatdeal of disease and ecological research as a result. To infer how landscape changes can affect host andparasite dynamics, a spatially explicit agent-based model is created to simulate movement and foraging ofthis primate, based on a resource landscape estimated from extensive plot-derived tree population data

ed colobuspatially explicit agent-based modelEIR modelisease transmissionibale National Park

from Kibale National Park, Uganda. Changes to this resource landscape are used to simulate effects ofanthropogenic forest change. With each change in the landscape, disease outcomes within the simulatedred colobus population are monitored using a hypothetical microparasite with a directly transmitted lifecycle. The model predicts an optimal distribution of resources which facilitates the spread of an infectiousagent through the simulated population. The density of resource rich sites and the overall heterogeneity

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ganda of the landscape are impdistribution are similar to

. Introduction

Increasing environmental change, driven by anthropogenicauses, is recognized as a major challenge to global health (Daszakt al., 2001; Patz et al., 2004; Jones et al., 2008). In the past 50ears, the size of the human population grew by 3.7 billion peo-le (Potts, 2007) and in the next 50 years the global population

s expected to surpass 9 billion people, with most of this growthccurring in the tropics (United Nations, 2009). This exponentialrowth of the human population forebodes many challenges tocological systems, and continued growth is predicted to exac-rbate the increasing demands for environmental products andervices (Houghton, 1994). Consequently, demand for resourcesas increased, bringing about large-scale alterations of environ-ental conditions for wildlife. While some effects are obvious

e.g., deforestation, fragmentation, and habitat loss), others areikely to be subtle and difficult to quantify (e.g., future ecosystem

omposition and host/vector interactions). These effects, althoughomplicated and difficult to generalize, are likely important driversf emerging infectious diseases (Daszak and Cunningham, 2003;lowright et al., 2008).

∗ Corresponding author. Tel.: +1 514 994 6541.E-mail address: [email protected] (T.R. Bonnell).

304-3800/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2010.07.020

t factors contributing to this spread. The characteristics of this optimale of logged sections of forest adjacent to our study area.

© 2010 Elsevier B.V. All rights reserved.

Species and populations in the order Primates are particu-larly suitable for investigating such complex issues because ofthe large amount of information already available on their ecol-ogy, and because primate species are in decline throughout theworld as a result of anthropogenic pressures (Chapman and Peres,2001; Struhsaker, 2005; Mittermeier et al., 2007). Habitat destruc-tion and hunting are thought to be the main factors driving thedeclines in primate populations (Mittermeier et al., 2007). How-ever, these same anthropogenic changes can also dramatically alterhost parasite interactions and are thus a concern for primate health(Formenty et al., 1999; Hahn et al., 2000; Graczyk et al., 2002;Chapman et al., 2005a; Goldberg et al., 2008b). The health of non-human primates is, in turn, of specific concern for human publichealth, due to the high risk that primates pose as reservoirs ofzoonotic pathogens (Wolfe et al., 2007; Davies and Pedersen, 2008).This is illustrated by such pathogens as the human immunode-ficiency virus (HIV; the cause of AIDS) (Hahn et al., 2000) andPlasmodium falciparum (the cause of virulent malaria) (Rich et al.,2009), both of which trace their origins to primates. In a recentstudy on the origins of major human infectious diseases, Wolfe et

al. (2007) found that even though non-human primates constitute0.5% of all vertebrates, their zoonotic transmission has contributedabout 20% of the major human infectious diseases.

Red colobus (Procolobus rufomitratus) of Kibale National Park,Uganda, offer an ideal modeling system for examining the effects

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f habitat change on primate disease dynamics. Forty years of long-erm data exist on their ecology, demography, and responses tonthropogenic change (Struhsaker, 1997; Chapman et al., 2005b).dditionally, the health of the red colobus has received consider-ble recent attention (Chapman et al., 2007; Goldberg et al., 2008a,009). This research has revealed evidence of transmission of dis-ase agents between red colobus and humans (Goldberg et al.,008b) and has highlighted the important role that fragmented

andscapes play in augmenting parasitism within the red colobusopulation (Gillespie and Chapman, 2006).

Our goal in conducting this research is to examine how thepatial distribution of resources in a forest habitat affects the trans-ission of parasites within a red colobus population. Based on

ecades of observations, we suspect resource distribution to influ-nce the transmission of parasites, based on observations of howed colobus use their habitats, where they choose to forage, howocial groups organize, and rates of contact between social groups.ed colobus live in social groups in which movement appear to be

argely driven by foraging for food. Red colobus are folivorous pri-ates, whose foods vary in spatial aggregation based on individual

ree species and on tree size (Chapman and Chapman, 2002). Theharacteristics of forests habitats are therefore important in deter-ining the amount and distribution of resources for these primates,

nd hence, movement behaviour of groups. To test ideas about howorest compositions, and therefore variation in the distribution ofhese resources, could affect disease transmission within a popula-ion of red colobus we created a simulation model. Our objectivesre then to use this simulation model to input a resource landscapepon which a simulated red colobus population, built with detailedehavioural data, can forage, allowing us to test landscape effectsn parasite transmissions at a population level.

To construct this simulation model, an agent-based modelingABM) framework was used (Grimm and Railsback, 2005; Senguptand Sieber, 2007). This approach has been used as an effectiveool in simulating primate group behaviour (Te Boekhorst andogeweg, 1994; Hemelrijk, 2002; Bryson et al., 2007; Sellers et al.,007), as well as infectious disease spread among primates (Nunnt al., 2008; Nunn, 2009). The overall construct of our model fol-ows previous theoretical constructs of agent-based models which

ere focused on spatially explicit epidemiological simulation (Bian,004; Roche et al., 2008). We also make use of recent softwaredvances linking ABM models with GIS (geographic informationystem) capabilities, allowing more detailed geographies to bencorporated implicitly, which allows these simulations to link spa-ial and temporal processes (Brown et al., 2005); for examples see,ennett and Tang (2006), Perez and Dragicevic (2009) and Kramer-chadt et al. (2009). Linking spatial and temporal processes haseen recognized as crucial for addressing questions regarding land-cape effects on disease (Ostfeld et al., 2005). In this case it allowss to link long-term forest data from our study area to a wealth ofehavioural and epidemiological data for red colobus.

.1. Study site and data collection

We focus on the red colobus living inside Kibale Nationalark, located in western Uganda. Kibale is composed of moist-vergreen forest (∼795 km2; 0◦ 13′–0◦ 41′ N and 30◦ 19′–30◦ 32′

), that receives approximately 1697 mm (1990–2009) of rain eachear distributed among two rainy seasons (Chapman and Chap-an, unpublished data). We focus on a subsection of the park

Kanyawara K-30 ∼250 ha) where detailed studies of red colobus

roup movement in relation to habitat quality have been conductedChapman et al., 2001; Chapman and Chapman, 2002; Snaith andhapman, 2005, 2008), as well as studies on forest properties forhe past 40 years (Struhsaker, 1997; Chapman et al., 2010). We useree data from three time periods (1989, 1999, and 2006), where

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26 plots (200 m × 10 m) were used to record identity and diameterat breast height (DBH) of trees larger than 10 cm DBH.

2. The model

The simulation model was developed using Repast Sim-phony 1.2.0 software (http://repast.sourceforge.net/) combinedwith open source GIS software from JTS (Vivid Solutions Inc.www.vividsolutions.com/jts). The model description follows theODD (Overview, Design concepts, Details) protocol for describingindividual- and agent-based models (Grimm et al., 2006).

2.1. Purpose

The purpose of the model is to test the effects that resourcedistribution has on parasite transmission within a population ofred colobus.

2.2. State variables and scales

The model is composed of three agents: the landscape, the host,and the microparasite. The model’s base is the landscape whereindividual resource polygons make up a grid surface. A scale of30 m × 30 m grids was chosen, as this roughly estimates the averagecanopy size of the trees in which a large proportion of the group willfeed, such that we assume foraging decisions are made at approx-imately this scale. Each polygon contains state variables, currentamount of resources, and maximum resource levels.

The host, red colobus, forages on this surface, represented asa point in a continuous space, moving from resource polygon toresource polygon and contains state variables, energy level, andthe number of neighbours needed to be considered safe from pre-dation. Each red colobus agent also contains spatial memory andbuilds its own list of remembered sites and estimates of resourcesat these sites, in real time. Additionally, the red colobus agent isconsidered to be in one of four states representing the progressionof disease, following a SEIR model (Hethcote, 2000). Specifically, thered colobus is either (S) susceptible to infection, (E) exposed but notyet infectious, (I) infectious to other hosts, and (R) recovered withimmunity developed against this disease.

The microparasite agent, with a maximum of one within ahost agent, can successfully infect another host, as determinedby a probability function based on distance to the next host. Themicroparasite agent contains state variables; host primate andmaturity level of infection. The microparasite characteristics weremodeled after a general class of parasites that are directly trans-mitted between hosts, through contact and proximity, in whichthere transmission probabilities are relatively high. We aim hereto represent the general behaviour of multiple classes of infectiousagents that are transmitted by direct contact, such as filoviruses,poxviruses, or retroviruses (the latter two of which have been doc-umented in Kibale red colobus (Goldberg et al., 2008a, 2009) orclose interactions (e.g., respiratory aerosols), such as metapneu-moviruses or respiratory syncytial viruses, which have recentlybeen shown to impact ape conservation across Africa (Kaur etal., 2008; Kondgen et al., 2008). We emphasize that we do notmodel any specific agent, but rather create a generalized frame-work that can be adapted to future efforts targeting specificagents.

The scale of the model is established so that one time step in

the model represents one half hour, in which red colobus agents,264 agents as part of 5 distinct social groups, forage on a 225 hagrid surface. The model is then run, starting with the infection ofone red colobus agent, until the microparasite agents goes extinctor the model reaches 6 months. The 6 months limit was chosen

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s population wide exposures, within our simulations, generallyccurred within this time period.

.3. Process overview and scheduling

The model is intended to simulate a novel parasite for whichhe primate hosts have no previous exposure. Time is modeledn discrete time steps, where each step is preformed in the sameequence. Each day is considered to be 26 half hour steps for a totalf 13 h, as red colobus are diurnal and are generally only activerom 07:00 to 20:00 (Struhsaker, 1975). A time step of half an houras chosen as this is the unit of measurement used in our long-

erm field observations of red colobus behaviour (Struhsaker, 1975;naith and Chapman, 2008). Within each time step, each primategent will, in turn, go through its steps, followed by the parasitegents. At the end of the step the resource agents perform a re-growtep (Fig. 1).

.4. Design concepts

The model is driven by the interaction between the landscape,

he red colobus, and the microparasite. The landscape affects theay in which the red colobus forage, including movement and con-

act rates between groups; movement and contact rates in turnffect transmission rates of the microparasite through the popula-ion.

ig. 1. Flow diagram outlining model processes and general scheduling of the models aecision tree described below (details on the decision tree are discussed in Section 2.6). S

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2.4.1. AdaptionThe red colobus agent is the only agent considered that dis-

plays adaptive behaviour. It can adapt to balance its needs to gainsafety within a group against the increased food competition expe-rienced by being a part of the group (Snaith and Chapman, 2008). Itaccomplishes this, within our model, by measuring its food intake.When there is sufficient food intake, the red colobus agent willvalue safety within the group; predation pressures are the assumeddriver behind the red colobus’ need for safety in numbers, however,there is no specific predation within the model. When food intake isless than the ideal, the primate is assumed to be more prone to takerisks and values feeding more than security within the group. Thisassumption is derived from the observation that red colobus groupstend to spread out during periods of food scarcity and contractduring periods of food abundance (Snaith and Chapman, 2008).

2.4.2. EmergenceRed colobus agents in the simulation model form part of a

specific social group, of which there are numerous groups in thesystem. Each group is only tied by mutual safety requirements,there are no other interactions (e.g., territoriality, intergroup dom-

inance), which is consistent with our current understanding ofred colobus socio-ecology (Struhsaker, 1975, 2010; Snaith andChapman, 2008). The lack of strict territorial behaviour is criticalfor our assumptions of how transmission will occur, as groups ofred colobus often forage within close proximity of each other, occa-

lgorithms. The model processes each type of agent separately; with each agent’shaded boxes represent an end point is reached in the decision tree.

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Fig. 2. Simulation environment: individual red colobus agents

ionally within the same tree, allowing for close contact and similarange use (Struhsaker, 2010). Foraging movements by an individualn the group affect others by limiting locations that are consideredafe or desirable. Through combined individual decisions, groupovement patterns are produced (Fig. 2).Disease spreads through the system through proximity of sus-

eptible host to infectious individuals. Within a specific social grouphe speed of the infection will spread based on the dynamics of theocial group, whereas inter group transmission is driven throughhared use of the forest landscape. Within the simulation modelhe driver behind both these transmission routes is the charac-eristics of the landscape and how they affect red colobus socialroups (i.e., group spread, shared resource sites, daily movementatterns). Through movement and foraging choices of these socialroups transmission between and within groups of the micropar-site agent leads to the emergence of host–parasite dynamics.

.4.3. SensingThe red colobus agent is assumed to know the values of the

esources and distances to all resource sites within their searchadius. They are also able to remember the location and quantityf past resource sites that contained a significantly higher amountf resources (i.e., spatial memory); it is assumed that the amountemembered at these resource sites will increases by the same re-row factor as the resource agent, allowing red colobus agents tostimate resource levels at these sites while not within their searchadius. The red colobus agent is also assumed to know the locationf other primates within its search radius. The microparasite andesource agents do not have any sensory capabilities.

.4.4. InteractionThe interaction between the host red colobus agent and a

icroparasite agent is defined by the microparasite. The micropar-site will change the status of the red colobus agent based on

resented by circles, resources are represented by grid squares.

its stage of development. It will also, at the end of its life cycleeither remove the host from the simulation (death) or give it a cer-tain amount of immunity (modeled as a resistance to subsequentinfections). Red colobus agents will also remove resources fromresource agents (polygons) lowering total resources available inthat resource agent for other red colobus agents.

2.4.5. StochasticityThe placement of a red colobus agent within a resource polygon,

once selected by the agent as a desired polygon to move towards,is randomly chosen, representing the limited information concern-ing fine scale within-group movements. The transmission of themicroparasite, from one agent to another, is then modeled as astochastic process in which proximity is a factor. This representsour uncertainty in the events leading to a successful transmissionfrom an infected host to that of a susceptible host. Stochasticity isalso included in determining the outcome of the infection, result-ing in the death of the host or the host acquiring a certain amountof immunity. Again this represents incomplete knowledge withrespect to factors leading to the death of a host.

2.5. Initialization

The primary input into the model is the distribution of redcolobus resources, in which we aim to reproduce distribution pat-terns observed at our study site. To accomplish this we use foreststructural data. We fit a pareto distribution, a statistical distri-bution used often to fit data showing a inverse J-shape, to theage class distribution of trees within our study site (Pareto shape

1.5185, location 10; Kolmogorov–Smirnov test; p < 0.05). A forestage class distribution is essentially a histogram classing individ-ual trees by their sizes, measured here by their diameter at breastheight (DBH). From these distributions we can estimate the dis-tribution of resources available to red colobus, assuming a direct

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elationship between DBH of trees and food availability. The rela-ionship between DBH and the availability of red colobus resourcess one that has been found at multiple sites (Chapman et al., 1992;overo and Struhsaker, 2007; Snaith and Chapman, 2008). Our for-st plot data showed a linear relationship between average DBHf a plot and the amount of red colobus food found within thatlot (Adjusted R square = 0.627, p < 0.01), collected from the 26orest plots. We were able to then populate our model environ-

ent, a 225 ha grid with 30 m × 30 m grid squares, with DBH valueselected from this fitted distribution. Each grid cell, now containingBH values, is then used as an estimate for the amount of resourcesvailable to the red colobus. By including a variable “DBHtoFood”o multiply the value of DBH within all sites, we are able to repro-uce the linear relationship between red colobus food and DBH. Bysing a fitted distribution to simulate forest stand structure (agelass distribution of forest trees) we are able to simply change thehape of the distribution to redistribute resources in our simulatednvironment, creating heterogeneous or homogeneous resourceandscapes, mimicking patterns seen at our study site. A final steps added where a common conversion factor is multiplied to eachesource cell to maintain equal amounts of resources between sim-lation runs.

This resource landscape is then populated with five distinctocial groups, of different sizes (70, 25, 84, 45, 40), as measuredy Snaith and Chapman (2008), representing average density of redolobus in our study area. The starting locations of these groups areandomly chosen, but fixed between runs. Each group is assignedith an initial memory of significant resource sites within an

xpected home range, based on data on group and home range sizeSnaith and Chapman, 2008). One individual from the same groups randomly chosen on the first step and becomes exposed at t = 1,nitiating the disease transmission process (see Table 1).

.6. Submodels

.6.1. Primate agent energy balanceA simple energy balance was created based on observations of

he time spent feeding by red colobus monkeys in the field. Within

ur study area, red colobus spend on average 43% of their time feed-ng (Snaith and Chapman, 2008). Thus, the assumption was madehat this represents their required food effort per day. Therefore, outf 26 steps, which represents one day in the simulation, approxi-ately 11 of these steps should be feeding events. By arbitrarily

able 1odel input parameters, both those calibrated and non-calibrated, included within the si

Agent Parameter Valu

Calibrated parameters (POM approach)Red colobus Energy gain per feeding 100/

Energy loss per step 100/Target energy level 100Search radius 100Safe radius GrouSafe neighbour size ± 5Significant DBH size 50Weight of known sites 2

Environment DBH to food 6Grow back rate 5Pareto location parameter 10

Microparasite Transmission: contact 2.5Transmission: droplet 1.25Transmission: airborne 0.62Incubation period 19Infectious period 6

Non-calibrated parametersEnvironment Pareto shape parameter 0.5–Microparasite Virulence 0–10

Immunity developed 0, 10

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choosing 100 as a target energy level, the energy gain per feedingmust be 100/11. The red colobus agent will also lose 100/26 unitsof energy each time step, mimicking metabolic requirements andwill result in a total loss of 100 units of energy each day, and areconsidered to be “hungry” when below the target energy level.

2.6.2. Primate agent safety rulesThe balance between safety and feeding competition, for the red

colobus agent, is accomplished by allowing the agent to modify itsparameter “safe neighbour size.” The number of neighbours that thered colobus agent needs to be considered safe will increase whenfeeding is successful and decrease when feeding targets are notbeing met. A primate agent considers itself safe when a sufficientnumber of its group members are nearby; where “nearby” is definedby a circle of radius X around the agent in question. The value of X isdetermined by a function of the red colobus’ social group size (saferadius = (1 m/individual) × group size), allowing individuals withinlarger groups to be aware of more group mates.

Each primate will measure its success in feeding by countingthe number of feeding events per day. If the primate is feedingon average 11 steps per day, i.e., 43% of the day as observed inour study area, then the number of neighbours to be consideredsafe is increased. If it is averaging less than 10 feeding steps perday the number of neighbours is lowered. The primate will alsodecrease safe neighbour size when energy levels are lower thanhalf the target energy level, indicating a stress period, and increasesafe neighbour size when energy targets are exceeded indicatingvery favourable conditions.

If the primate agent does not consider itself in a safe position,i.e., not enough neighbours nearby, it will move towards its socialgroup. It does this by locating its closest group members, consider-ing only the number of neighbours it needs to be considered safe,and moves to the center of that group. If the center of these nearbymembers is farther than 50 m it the agent will move 50 m towardsthat center. This value of 50 m is based on observations that onerarely sees animals further than this from other group membersand this value is thought to be approximately the limit with whichan individual could visually see another group member through the

canopy (Chapman, unpublished data).

2.6.3. Primate agent foraging rulesPrimates forage by choosing the best food site based on a sim-

ple rule comparing the distance to the food site and the amount of

mulations.

e Units References

11 Energy Snaith and Chapman (2008)26 Energy Snaith and Chapman (2008)

Energy Snaith and Chapman (2008)Meters –

p size Meters –Agents –cm –– –Energy/DBH –Energy/step –– Chapman (unpublished data)% –% –

5 % –Days Hutin et al. (2001)Days Hutin et al. (2001)

4.0 – Chapman (unpublished data)0 % –0 % –

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esource at the site. A food site index is created, using this rule, tollow a red colobus agent to choose the best site from sites consid-red to be safe (Boyer et al., 2006; Ramos-Fernandez et al., 2006).ood sites are considered safe if, once moved, the agent would havenough neighbours nearby.

ood site index = distance (m)food (energy)

est food site = min(food site index)

Once a food site is chosen, the red colobus agent will then moveowards it. If the food site is contained within the agent’s searchadius, the agent is assumed to move directly to the site. If theesired food source is beyond this threshold (i.e., from a remem-ered site), then the agent will move towards it, choosing a safeite by again comparing food sites with the food site index, usinghe distance to the remembered site as a factor.

We also included a variable, “weight of known sites”, to allowemembered sites to potentially have more draw when choos-ng possible food sites. This represents our assumptions that redolobus use spatial memory in making foraging decisions and willavour past sites in which they have had successful feeding. Thealue of “weight of known sites” is divided from the food site indexf a remembered site, thereby increasing its attraction to a redolobus agent (i.e., if “weight of known sites” is set to 2 a remem-ered site will be 2 times more attractive than a non-rememberedite of equal resources and distance).

The amount of spatial memory used by a red colobus agent wasontrolled with the variable “significant DBH”. If any resources siteas above this value the red colobus considered it to be a significant

ite and would add it to its list of remembered sites. By increasingnd decreasing the significant DBH value we could correspondinglyncrease or decrease the amount of memory used by the red colobusgent in making foraging decisions.

.6.4. Microparasite transmissionThe microparasite agent within our model is able to replicate

tself in nearby hosts, where the success of transmission is a func-ion of the distance to other hosts. This function is representedere as a discrete function representing probability of transmissionased on stages in hosts proximity, modeling transmission routesf contact, droplet range (from coughing/sneezing), and finally air-orne exposure. Parameters values for transmission probabilitiesere estimated by, starting from low values (close to zero), increas-

ng the probability of transmission until population wide exposuresere possible within our simulation, modeling a highly contagiousathogen.

robability of transmission (distance = x)

={

If x ≤ 2.5 m pcontac = 0.025%If 2.5 m < x < 5 m pdroplet = 0.0125%If 5 m < x < 10 m pairborne = 0.00625%

Once transmission occurs, the new microparasite agent will ageuring its incubation period only becoming infectious after the

ncubation period has elapsed. At the end of the infectious periodhe microparasite’s virulence parameter will determine the prob-bility that the microparasite will kill the host, in which case both

he host and microparasite are removed from the simulation. Thisepresents the only source of mortality in the model. We assumeere that virulence is independent of the mode of transmission andhat the infection and incubation times are relatively static (seeramer-Schadt et al., 2009 for discussion).

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2.6.5. Resource agent re-grow rateThe resource agent (grid square) holds a certain amount of

resources, which the red colobus can “eat” and deplete (Snaith andChapman, 2005). A resource agent, if reduced by foraging, is able tothen re-grow at a constant rate (“grow back rate”) every time step,until it reaches its set maximum resource level; which is its initialvalue at the start of the simulation.

2.7. Model predictions and observations

To parameterize and build the model we employed “modelcycling” with a pattern orientated modeling (POM) approach(Grimm and Railsback, 2005; Kramer-Schadt et al., 2007). With this,we compared patterns of behaviour from our model to selectedperformance criteria that we have defined. These selected perfor-mance criteria were geared towards aspects of the system whichwe thought were essential in determining transmission rates, con-sisting of: monthly home range size of red colobus groups, averagedaily group movement, and their average spread.

Simulated groups of red colobus that followed simple rules bal-ancing safety requirements against increased food competition,were able to reproduce expected trends observed in the field: largergroups foraged over larger home ranges, traveled longer distancesper day, had a larger group spread and needed to spend more timemoving per day than smaller groups (Snaith and Chapman, 2008;Chapman and Chapman, 2000). In lower quality habitats, groupsincreased their home ranges, travel distance per day, group spread,and time spent moving per day. These trends are consistent withempirical data on group movement patterns when habitat qual-ity has been taken into account (Chapman et al., 2006; Snaith andChapman, 2008). These patterns held for a wide variety of resourcelandscapes, as well as different parameterizations of our assumeddecision rules. This suggests that our assumptions have capturedimportant components of primate group movement and behaviour.To verify that our simulation could adequately reproduce move-ment behaviours, we attempted to parameterize the simulation toreproduce the performance criteria for a group of 70 individuals.Compared to our observed data (simulated value/observed value),we were able to test the fit of our models; 86% for average monthlyhome range, 75% for average day range, and 67% for average groupspread. As a validation step, we varied group size without chang-ing parameterization and compared the simulated results to ourobserved field data (Fig. 3). The model was able to reproduce trendsin our observed data, suggesting that our model has captured manyelements of group movement behaviour in red colobus groups.

If we examine our model, overall the values for our performancecriteria were consistently underestimated. We attribute this to twopotential factors. First, during our calibration and construction ofthe model, we focused on one group of 70 individuals, and didnot take increased movement due to food competition from mul-tiple group scenarios into account. We also attribute some of theunderestimations to be due to our relatively simple rules governingsocial interactions between individuals of a group. The omissionof ranking or demographics in our social groups somewhat com-plicates group movement behaviour within the model, as everyprimate agent has the same weight in group movement decisions,causing what seems to be, in some cases, indecision in group move-ment. With the inclusion of higher ranked individuals or groupdemographics, we might be able to better fit model predictions toobservations in average daily movements and home range sizes.

We also found patterns that we did not expect in the simulated

groups, but are seen in wild populations of red colobus. Observa-tions in the field have been made of groups, mostly large groups,breaking into smaller subgroups temporarily to forage separately,and then re-group. This is termed fission–fusion of groups (Aureli etal., 2008). With our simple assumptions regarding the trade-off of

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Fig. 3. Model predictions of performance criteria (average monthly home range,atbt

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est characteristics that described the distribution of resources and

verage spread of group and average daily movements) while holding environmen-al variables constant and only varying group size. Observed values are representedy squares, and diamonds represent simulated values. Simulations results followrends in observed data.

afety and food competition within a group, we see fission–fusionynamics in simulated groups undergoing food stress, in such casess; large groups (∼100+ individuals) or with groups in low resourceandscapes.

. Results

When the simulation was run the microparasites spread withinocial groups, showing a continuous cycling when immunity wasot developed and only once when immunity was developed. Welso observed the microparasite spread between social groups. Byarying forest composition and hence the distribution of resourcesithin the simulation, we were able to test how changes in resourceistribution could affect transmission rates in red colobus popula-ions.

Spatial memory, “SigDBH”, was found to be an important factor,nfluencing the direction of the effects of the landscape. When thepatial memory of groups was not considered in the simulations,reating more homogeneous landscapes increased the rangingehaviour of primate groups, consistently increasing the probabil-

ty that groups would contact each other. However, when spatialemory was considered in the model, transmission rates were

verall consistently higher, and revealed contrary results. Whenpatial memory was considered in the simulations, highly homo-eneous landscape had relatively lower contact rates; with the

ate of contact between groups increasing with increasing resourceeterogeneity. However at a point, in highly heterogeneous land-capes, the probability of contact between groups decreased. Thishift from an increase to a decrease in the rate of contact can be seen

Fig. 4. Effects of density of high resource sites on the probability of contact betweengroups. The probability of contact is estimated from the percentage of simulationsin which all groups became infected by the microparasite (simulation results froma total of 297 runs).

as a reflection of the number of remembered sites held in commonbetween groups. In landscapes with higher number of significantsites, a large number of resources are shared by multiple groups,such that two or more groups will choose the same site at a giventime only rarely. This probability of contact increases as the numberof sites decreases, allowing for smaller shared memories of signifi-cant sites and an increased chance of two or more groups choosingto visit the same site at the same time. As shared memory decreasesfurther, eventually approaching zero, the probability of contactingother groups begins to decrease; reaching levels of transmissionsimilar to model runs without spatial memory. Our model there-fore predicts that the density of high resource sites influences theprobability of contacting other groups (Fig. 4).

The cost of the parasite to the host, modeled here as the proba-bility that the parasite will kill the host after its infectious period,had an effect on overall transmission within the population of redcolobus hosts. When immunity to the parasite was not acquired bythe hosts, highly virulent microparasites increase overall popula-tion survival; with maximum population loss at an intermediatevirulence value. At higher virulence, infectious hosts die beforebeing able to infect other hosts, while also reducing the size of theirgroups and hence reducing their groups’ movement. This is some-what expected from epidemiological theory, regarding parasitesthat are reliant on their host movement for transmission success(Ewald, 1995). In regards to how the distribution of resourcesaffects this trade-off we find that the virulence value in whichthe population is reduced the most shifts as the distribution ofresources facilitates overall contact rates within the population,enabling more virulent strains to have a greater impact on thepopulation as well as to spread over larger areas (Fig. 5).

4. Discussion

Insights from this model focusing on the effects of changingresource distributions lead us to predict that resource clumpingwithin habitat patches is likely to be an important factor affectingtransmission rates within populations of animals that use patchyenvironments. Many animal species, including red colobus, use spa-tially aggregated resources, suggesting that this may represent ageneral phenomenon. The model also highlights the fact that trans-mission rates would be spatially dependant, with certain parts ofthe landscape being hot spots of transmission, such as habitats withfew high resource sites.

To generalize our results, we found that there were two for-

created spatial “hot spots” of transmission: (1) overall variation inforest tree age classes and (2) the number of high resource sites. Theformer represented a level of heterogeneity in the forest, whereasthe latter represented the effects of shared resource sites; both

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Fig. 5. Effects of varying resource distribution on (a) overall population survivalrates, and (b) spread of the microparasite (ha). The environmental metric, paretosWar

atrtpiahaebtiddi

mmasfmlset

ncto

hape parameter, is used to modify the distribution of resources in the simulation.e see that population survival is lower and overall microparasite spread is higher

t an optimal resource distribution (pareto shape parameter: 1.5). (Simulation wasun a minimum of 300 times for each environmental metric: 0.5, 1.5, 2.0, and 3.0).

re not entirely independent of each other. These two characteris-ics represented two different processes, and their different effectseflect the different spatial scales on which they operate. Changeso the level of heterogeneity of the landscape affects the foragingatterns of groups at the scale of neighbouring resources, influenc-

ng short range movement patterns and overall spread of the groupsnd effecting transmission dynamics within the group. On the otherand, the number of high resource sites affects foraging patternst spatial scales closer to that of a group’s home range, influ-ncing long range movement patterns and affecting transmissionetween groups. The relative importance of these two characteris-ics in determining overall parasite transmission was determinedn our simulation by the importance that spatial memory plays inetermining red colobus movement patterns, suggesting that theensity of high resource sites would be the most significant factor

n determining the spread of the microparasite.Species of non-human primates are thought to retain spatial

emory with which they develop cognitive maps of their environ-ents resources (Poucet, 1993; Di Fiore and Suarez, 2007; Janson

nd Byrne, 2007). Our model suggests that resources sites which arehared in memories of individuals in a group would be importantor the transmission of disease. We therefore predict that a species

ay limit its contact with other groups by following different evo-utionary strategies, such as developing territoriality or holdingtrong preference for familiar feeding sites. We might thereforexpect that in heavily parasitized communities, factors that reducehe similarities of inter group cognitive maps might be selected.

If we apply the simulation results to our specific study site, toearby areas that were selectively logged in the late 1960s, we canompare forest structure characteristics of undisturbed and dis-urbed areas. We observe a general trend between the intensityf logging and a decrease in the proportion of large trees and an

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increase in the proportion of mid-sized trees. This suggests thatlogged areas, with little to no large trees, will produce a resourcelandscape with very few high values food sites, whereas unloggedareas consist of many high value resource sites. From our plot data(5 plots within logged area; 11 from the undisturbed area) we gainan estimate of significant resource sites (trees > 50 cm DBH) withineach area: unlogged 39.5 significant sites/ha, logged 18 significantsites/ha. From the results of our model we would predict that, in thelogged areas, the density of resources would act to increase trans-mission rates between groups leading to less variation in diseasestates among groups and possibly an increase in the intensity ofparasitism. However, it must be noted that this prediction relieson the assumption that the estimated high value resource sites arerandomly distributed and that host densities are similar in bothareas, as well as that logging does not induce other stressors thatcould influence immunity (e.g., a decrease in available foods).

GIS capabilities were embedded and used within our agent-based model, following past approaches which have highlightedthe benefits of ABM/GIS systems (Brown et al., 2005). The GIS capa-bilities allowed us to develop a complex landscape on which wecould run our individual based SEIR model, similar to approachestaken by Linard et al. (2009), and to apply such a model in the con-text of an important wildlife host–parasite system. As long as thecontext considered is a general one (e.g., organisms using patchyresources), then the model will be broadly applicable to a numberof wildlife-disease interactions.

The fact that red colobus group movements and foraging pat-terns are closely associated with environmental characteristics(Snaith and Chapman, 2008), creates an opportunity to simulatehow changes to environmental characteristics can affect aspects ofhost parasite interactions within a population. A similar approach,using detailed environmental data along with behavioural data,should be applicable to other host–parasite systems as well. Exam-ples of systems that would benefit from these approaches mightbe: (1) directly transmittable parasites reliant on a mobile hostfor transmission, where connectivity amongst the host populationis determined from landscape properties (e.g., rabies), (2) para-sites who have a life stage in the external environment and arerelatively immobile, where overlap and range use of the defini-tive host would be an important (e.g., gastro-intestinal parasites),(3) parasites in which a specific host is responsible for spread-ing disease amongst separate reservoir populations (e.g., Lymedisease, poxviruses, ebola virus). The value of our study is there-fore not only to predict how disease transmission in red colobusin Kibale might respond to changing forest structure, but also toprovide ground work for predicting similar effects in other hostspecies where environmental characteristics are important driversaffecting transmission of parasites. Predictions from such modelsshould be useful in constructing informed management plans forendangered species that account for the transmission of infectiousdisease across real landscapes (depicted with remote sensing data),as well as for predicting the disease-related effects of a changingclimate, habitat fragmentation, logging, or other similar anthro-pogenic changes to wildlife habitats.

Acknowledgements

Funding for the Ugandan research was provided by CanadaResearch Chairs Program, Wildlife Conservation Society, NaturalScience and Engineering Research Council of Canada, National

Geographic, and the National Science Foundation to CC, and bythe Morris Animal Foundation through its support of the KibaleEcoHealth Project (award #D07ZO-024) and the University of Wis-consin School of Medicine and Public Health from The WisconsinPartnership Program to TG. Support for the modeling work was

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rovided by Natural Science and Engineering Research Council ofanada (RS, CC). Permission to conduct the research in Ugandaas given by the National Council for Science and Technology and

he Uganda Wildlife Authority. We would like to extend a spe-ial thanks to Mel Lefebvre, Lauren Chapman, Julian Zhunping,nd Andre Costopoulos for helpful comments on this manuscript,s well as to Margaret Kalácska for providing access to computeresources.

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